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find the first 3 terms in the expansion of (x+4)(1+3x)^-2 as a series in ascending powers.

I expanded the second bracket using binomial expansion and got 1 -6x +27x^2 -108x^3

how do I combine (x+4) with the expansion?

Any help would be appreciated.

  • maths -

    just multiply out as usual, taking only the firet 3 terms:

    (1 -6x +27x^2 -108x^3)(4+x)
    = (1 -6x +27x^2 -108x^3)*4
    + (1 -6x +27x^2 -108x^3)*x

    = 4 - 24x + 108x^2 - ...
    + x - 6x^2 + 27x^3 - ...
    ----------------------------------
    4 - 23x + 102x^2 + ...

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